A Note on Occam's Razor

Occam's razor is often justified on the grounds that our world is simple, as proved by fundamental physics. Equally often, Occam is declared wrong on the grounds that there is complexity in the world, for instance in biology. In both cases, Occam's razor is interpreted as a statement about the world, rather than a principle of scientific method. In his compelling discussion of Hume's problem (Nature 366, 105-106; 1993), Allan Goddard Lindh reopens this issue. My view is that the interpretation of Occam's razor as a statement about the world is of no interest to the practising scientist. This argument does not involve any new philosophical idea.

A careful reading of Occam's statements "Plurality is not to be assumed without necessity" and "What can be done with fewer assumptions is done in vain with more" (my italics), shows that Occam's principle is independent of the nature of the world: in any possible universe, we should seek the simplest feasible interpretation of our observations, even though this interpretation may be very complex in absolute terms. As an example, a double helix is more complex than a single helix, but it is still the simplest structure that can account for what is known about DNA and heredity. No doubt an explanation involving a more complex structure could be contrived, but it is not necessary.

As Karl Popper pointed out in The Logic of Scientific Discovery, Occam's razor is a consequence of the requirement that hypotheses be falsifiable: if a theory contains fewer parameters than the facts that it can predict, then the theory has already been corroborated. For instance, if ten points on a graph lie on a straight line, then the straight-line hypothesis could have been falsified eight times, but was not. In this case, a falsificationist application of Occam's razor requires that we accept the straight line as a working hypothesis, extrapolate from it, and test its predictions; it does not require accepting the straight line uncritically.

There are two other methodological reasons to seek simplicity: simple models are easier to simulate and they give more insight into the processes that one is trying to understand. However, I believe that the greater falsifiability of simpler hypotheses is the main reason why, in any possible world, we can do no better than trying out the simplest hypothesis first, independently of whether it is more likely to be true.